Finite Group Databasebeta

← Group #13167060

Character table — Group #13167060

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222224444444444444444444444888888888888889999121212121212121212121212181818181818181818181818181824242424242424242424242436363636363636363636108108108108
order124423461212333366666661212121212121212121212366666612121212121212224488882424242424242424246688888888121224242424242424242424242461224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111-11-11111111-1-1-11111-1-1-1111111111-1-1-1-1-11-1-1-111-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111-11-11111111-1-1-11111-1-1-1111111111-1-1-1-1-11-1-1-111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111-11-11111111-1-1-11111-1-1-1111111111-1-1-1-1-11-1-1-111-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ81111-11-11111111-1-1-11111-1-1-1111111111-1-1-1-1-11-1-1-111-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ911-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1i−ii−iii−i−iii−i−i1-111ii−i−iii−i−i-1-1iii−i−i−iiii−i−i−i1-1ii−i−iii−i−i1-11-1
χ1011-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1i−ii−iii−i−iii−i−i1-111−i−iii−i−iii-1-1iii−i−i−iiii−i−i−i1-1−i−iii−i−iii-11-11
χ1111-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1−ii−ii−i−iii−i−iii1-111ii−i−iii−i−i-1-1−i−i−iiii−i−i−iiii1-1ii−i−iii−i−i-11-11
χ1211-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1−ii−ii−i−iii−i−iii1-111−i−iii−i−iii-1-1−i−i−iiii−i−i−iiii1-1−i−iii−i−iii1-11-1
χ1311-1-1-1111-1-11111-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1i−i−iiii−i−i−i−iii-1111ii−i−i−i−iii-1-1iii−i−i−i−i−i−iiii-11ii−i−i−i−iii1-1-11
χ1411-1-1-1111-1-11111-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1i−i−iiii−i−i−i−iii-1111−i−iiiii−i−i-1-1iii−i−i−i−i−i−iiii-11−i−iiiii−i−i-111-1
χ1511-1-1-1111-1-11111-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1−iii−i−i−iiiii−i−i-1111ii−i−i−i−iii-1-1−i−i−iiiiiii−i−i−i-11ii−i−i−i−iii-111-1
χ1611-1-1-1111-1-11111-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1−iii−i−i−iiiii−i−i-1111−i−iiiii−i−i-1-1−i−i−iiiiiii−i−i−i-11−i−iiiii−i−i1-1-11
χ172222222222222222222222222222222222222222222222-2-2-2-2000000000000-2-2-2-200000000-2-2000000000000-2-2000000000000
χ1822222-12-1-1-122-1-1-12222-1-1-12222-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-100000000-1-12-1-12-1-12-1-12-1-1-1-1000000000000
χ1922222-12-1-1-122-1-1-12222-1-1-12222-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-12222-2-2-2-21111111122-1-100000000-1-1-211-211-211-211-1-1000000000000
χ2022222-12-1-1-122-1-1-12222-1-1-12222-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3-2-21100000000110−i3i30−i3i30−i3i30−i3i311000000000000
χ2122222-12-1-1-122-1-1-12222-1-1-12222-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3-2-21100000000110i3−i30i3−i30i3−i30i3−i311000000000000
χ222222-22-22222222-2-2-22222-2-2-2222222222-2-2-2-2-22-2-2-222-2-2-2-2-2-200000000000022-2-200000000-2-200000000000022000000000000
χ232222-2-1-2-1-1-122-1-11-2-222-1-11-2-222-1-1-1-122-1-21111-1-211-1-111222222-2-2-1-1-1-11111-2-2-1-100000000-1-12-1-12-1-1-211-21111000000000000
χ242222-2-1-2-1-1-122-1-11-2-222-1-11-2-222-1-1-1-122-1-21111-1-211-1-1112222-2-2221111-1-1-1-1-2-2-1-100000000-1-1-211-2112-1-12-1-111000000000000
χ252222-2-1-2-1-1-122-1-11-2-222-1-11-2-222-1-1-1-122-1-21111-1-211-1-111-2-2-2-20000−i3i3−i3i3i3−i3i3−i3221100000000110−i3i30−i3i30i3−i30i3−i3-1-1000000000000
χ262222-2-1-2-1-1-122-1-11-2-222-1-11-2-222-1-1-1-122-1-21111-1-211-1-111-2-2-2-20000i3−i3i3−i3−i3i3−i3i3221100000000110i3−i30i3−i30−i3i30−i3i3-1-1000000000000
χ2722-2-222-22-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-222000000000000-22-2-20000000022000000000000-22000000000000
χ2822-2-22-1-2-11122-1-1-12222-1-11-2-2-2-21111-2-2-12-1-1-1-1-1-211111122-2-22i−2i2i−2i−i−iii−i−iii2-2-1-100000000112i−i−i−2iii2i−i−i−2iii-11000000000000
χ2922-2-22-1-2-11122-1-1-12222-1-11-2-2-2-21111-2-2-12-1-1-1-1-1-211111122-2-2−2i2i−2i2iii−i−iii−i−i2-2-1-10000000011−2iii2i−i−i−2iii2i−i−i-11000000000000
χ3022-2-22-1-2-11122-1-1-12222-1-11-2-2-2-21111-2-2-12-1-1-1-1-1-2111111-2-22200003−3−333−3−33-221100000000-1-103−30−3303−30−331-1000000000000
χ3122-2-22-1-2-11122-1-1-12222-1-11-2-2-2-21111-2-2-12-1-1-1-1-1-2111111-2-2220000−333−3−333−3-221100000000-1-10−3303−30−3303−31-1000000000000
χ3222-2-2-2222-2-22222-2-2-22222222-2-2-2-2-2-2-2-22-2-2-2-2-22222-2-222-2-2220000000000002-2-2-200000000220000000000002-2000000000000
χ3322-2-2-2-12-11122-1-11-2-222-1-1-122-2-21111-2-2-1-21111-12-1-111-1-122-2-22i−2i−2i2i−i−iiiii−i−i-22-1-100000000112i−i−i−2iii−2iii2i−i−i1-1000000000000
χ3422-2-2-2-12-11122-1-11-2-222-1-1-122-2-21111-2-2-1-21111-12-1-111-1-122-2-2−2i2i2i−2iii−i−i−i−iii-22-1-10000000011−2iii2i−i−i2i−i−i−2iii1-1000000000000
χ3522-2-2-2-12-11122-1-11-2-222-1-1-122-2-21111-2-2-1-21111-12-1-111-1-1-2-22200003−3−33−333−32-21100000000-1-103−30−330−3303−3-11000000000000
χ3622-2-2-2-12-11122-1-11-2-222-1-1-122-2-21111-2-2-1-21111-12-1-111-1-1-2-2220000−333−33−3−332-21100000000-1-10−3303−303−30−33-11000000000000
χ372-22i−2i020-22i−2i2222000-2-2-2-20002i−2i2i2i−2i−2i2i−2i200000-20002i−2i002-22i−2i000000000000002-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ382-22i−2i020-22i−2i2222000-2-2-2-20002i−2i2i2i−2i−2i2i−2i200000-20002i−2i002-22i−2i000000000000002-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ392-22i−2i020-22i−2i2222000-2-2-2-20002i−2i2i2i−2i−2i2i−2i200000-20002i−2i00-22−2i2i00000000000000-222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ402-22i−2i020-22i−2i2222000-2-2-2-20002i−2i2i2i−2i−2i2i−2i200000-20002i−2i00-22−2i2i00000000000000-22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i00000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ412-2−2i2i020-2−2i2i2222000-2-2-2-2000−2i2i−2i−2i2i2i−2i2i200000-2000−2i2i002-2−2i2i000000000000002-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ422-2−2i2i020-2−2i2i2222000-2-2-2-2000−2i2i−2i−2i2i2i−2i2i200000-2000−2i2i002-2−2i2i000000000000002-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ432-2−2i2i020-2−2i2i2222000-2-2-2-2000−2i2i−2i−2i2i2i−2i2i200000-2000−2i2i00-222i−2i00000000000000-22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i00000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ442-2−2i2i020-2−2i2i2222000-2-2-2-2000−2i2i−2i−2i2i2i−2i2i200000-2000−2i2i00-222i−2i00000000000000-222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ4544444444441-2114-2-21-2114-2-2111111-2-2-2111-2-2-2111-2-2-2-2000022222222222200000000000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ4644444444441-2114-2-21-2114-2-2111111-2-2-2111-2-2-2111-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000000000000011111111111100000000000000
χ474444444444-21-2-2411-21-2-2411-2-2-2-2-2-2111-2-2-2111-2-2-2111100000000000000000000222222220000000000000000-1-1-1-1-1-1-1-10000
χ484444444444-21-2-2411-21-2-2411-2-2-2-2-2-2111-2-2-2111-2-2-2111100000000000000000000-2-2-2-2-2-2-2-20000000000000000111111110000
χ4944444-24-2-2-21-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2-211−1−3i32−1+3i321111−1−3i32−1+3i32111100002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300000000000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ5044444-24-2-2-21-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2-211−1−3i32−1+3i321111−1−3i32−1+3i3211110000-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i3000000000000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ5144444-24-2-2-21-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2-211−1+3i32−1−3i321111−1+3i32−1−3i32111100002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300000000000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ5244444-24-2-2-21-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2-211−1+3i32−1−3i321111−1+3i32−1−3i3211110000-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i3000000000000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ534444-44-44441-211-4221-211-422111111-2-2-2-1-1-122-2-1-1-1-2-222000022-2-22222-2-2-2-200000000000000-1-1-1-1-1-111111100000000000000
χ544444-44-44441-211-4221-211-422111111-2-2-2-1-1-122-2-1-1-1-2-2220000-2-222-2-2-2-2222200000000000000111111-1-1-1-1-1-100000000000000
χ554444-44-4444-21-2-2-4-1-1-21-2-2-4-1-1-2-2-2-2-2-2111222-1-1122211-1-1000000000000000000002222-2-2-2-20000000000000000-1-1-1-111110000
χ564444-44-4444-21-2-2-4-1-1-21-2-2-4-1-1-2-2-2-2-2-2111222-1-1122211-1-100000000000000000000-2-2-2-2222200000000000000001111-1-1-1-10000
χ574444-4-2-4-2-2-21-2−1−3i32−1+3i322221-2−1−3i32−1+3i3222211−1−3i32−1+3i32−1−3i32−1+3i32-2-21-11+3i321−3i32-1-11-11+3i321−3i3211-1-1000022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000000000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ584444-4-2-4-2-2-21-2−1−3i32−1+3i322221-2−1−3i32−1+3i3222211−1−3i32−1+3i32−1−3i32−1+3i32-2-21-11+3i321−3i32-1-11-11+3i321−3i3211-1-10000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ594444-4-2-4-2-2-21-2−1+3i32−1−3i322221-2−1+3i32−1−3i3222211−1+3i32−1−3i32−1+3i32−1−3i32-2-21-11−3i321+3i32-1-11-11−3i321+3i3211-1-1000022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000000000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ604444-4-2-4-2-2-21-2−1+3i32−1−3i322221-2−1+3i32−1−3i3222211−1+3i32−1−3i32−1+3i32−1−3i32-2-21-11−3i321+3i32-1-11-11−3i321+3i3211-1-10000-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ6144-4-444-44-4-41-2114-2-21-211-422-1-1-1-1-1-122-2111-2-2-2-1-1-1222200002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000−i−i−iiii−i−i−iiii00000000000000
χ6244-4-444-44-4-41-2114-2-21-211-422-1-1-1-1-1-122-2111-2-2-2-1-1-122220000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000iii−i−i−iiii−i−i−i00000000000000
χ6344-4-444-44-4-4-21-2-2411-21-2-2-4-1-1222222-1-11-2-2-2111222-1-1-1-1000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000−i−iii−i−iii0000
χ6444-4-444-44-4-4-21-2-2411-21-2-2-4-1-1222222-1-11-2-2-2111222-1-1-1-100000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000ii−i−iii−i−i0000
χ6544-4-44-2-4-2221-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32222-1-11+3i321−3i321+3i321−3i322211−1−3i32−1+3i32111-11+3i321−3i32-1-1-1-100002i−2i2i−2i2ζ222ζ14−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ1400000000000000−i−ζ22−ζ14iζ22ζ14−i−ζ22−ζ14iζ22ζ1400000000000000
χ6644-4-44-2-4-2221-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32222-1-11+3i321−3i321+3i321−3i322211−1−3i32−1+3i32111-11+3i321−3i32-1-1-1-10000−2i2i−2i2i−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ142ζ222ζ1400000000000000iζ22ζ14−i−ζ22−ζ14iζ22ζ14−i−ζ22−ζ1400000000000000
χ6744-4-44-2-4-2221-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32222-1-11−3i321+3i321−3i321+3i322211−1+3i32−1−3i32111-11−3i321+3i32-1-1-1-100002i−2i2i−2i2ζ142ζ22−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ2200000000000000−i−ζ14−ζ22iζ14ζ22−i−ζ14−ζ22iζ14ζ2200000000000000
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χ6944-4-4-4444-4-41-211-4221-2114-2-2-1-1-1-1-1-122-2-1-1-122-211122-2-200002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000−i−i−iiiiiii−i−i−i00000000000000
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χ1018-8−8i8i0-4044i−4i-422206-64-2-2-20−6i6i4i−4i−2i−2i2i2i−2i2i-1000-331000i−i3i−3i00000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i0-4044i−4i-42220-664-2-2-206i−6i4i−4i−2i−2i2i2i−2i2i-10003-31000i−i−3i3i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.